Studies on Beam Formation
in an Atomic Beam Source
Why don‘t we understand the intensity output of an ABS?
Alexander Nass, Erhard Steffens
University of Erlangen-Nürnberg, Germany
Michelle Stancari
INFN, Ferrara, Italy
SPIN 2008, Charlottesville,VA,USA, Oktober 6, 2008
Atomic Beam Source (ABS)
 Production of polarized H or D beams
for polarized gas targets and polarized
ion sources
 H gas expands through cooled nozzle
and forms of high brightness beam with
skimmer and collimator
 Sextupole magnets focus beam and
produce electron polarization
 HF - transitions  nuclear polarization
 Output intensity of the sources not
understood
Supersonic Gas Expansions
 Free jet atomic or molecular beam from supersonic gas expansion
from a high-p source (p0) into a low-p background (pb)
 Gas accelerates during expansion and beam temperature decreases
 If pb small  smooth transition to molecular flow, no shock stuctures
Thermodynamics
 Energy equation of an ideal expanding gas without viscous and
heat conduction effects:
h0 = h+v2/2
 For ideal gases (dh = cp dT) and constant cp= (g / (g-1))kB/m) one
gets the maximum or terminal velocity:
v 
2k B  γ 

T0
m  γ 1 
 For more information see D.R.Miller in: G.Scoles (Ed.), Atomic and
Molecular Beam Methods, Vol.I (Oxford Univ. Press, 1988) 14
 Some properties can be calculated, but in general models are
needed to describe the beam parameters
Example: H2 (D2) expansion at
T0=100 K (g=5/3)
 vH2 = 1436 m/s
 vD2 = 1015 m/s
Direct Simulation Monte Carlo Method
(DSMC)
 Technique for computer modeling of a real gas by some thousands or
millions of simulated particle trajectories
 Particles are followed through representative collisions and boundary
interactions in space
 Key assumptions: decoupling of the motion and collisions of particles
over small time steps and division of the flow field into small cells
 Therefore: time steps << mean collision time
cell dimensions << local mean free path
 More information on the method see: G.A.Bird, Molecular Gas
Dynamics and the Direct Simulation of Gas Flows (Clarendon Press
Oxford, 1994)
Direct Simulation Monte Carlo Method
(DSMC)
 Geometry of the beam forming elements in an ABS are implemented
as boundary walls with temperature T for an axially symmetric flow
 Regions 1-7 are divided into small cells
 The Stream Input flow is inflowing H gas and the Specified flows
compensate for flow losses at the boundaries of regions 3 and 6
Experimental Setup




Microwave dissociator with a 2,45 GHz surface wave
Beam profile monitor for intensity measurements
Fast chopper and QMS for velocity analysis
Determination of the degree of dissociation with the QMS:
S*a
α *
Sa  2κ ion κ det κ vSm
Velocity Analysis
 Velocity distribution determined with TOF-method with a fast chopper
cutting out a beam package and detection with a QMS
 Deconvolution of the measured distribution to remove the influence of
the chopper opening function and the electronics
 Resulting function is
fitted to extract beam
parameters
(p2=Tx, p3=vx):
2

l
 
p1
m  cq

  p3  
F(t)  2 exp 
t
 2k B p 2  t
 
Molecular Hydrogen Expansions
 DSMC calculation of an H2 expansion with a flow of Q=1 mbarl/s and
a nozzle temperature Tnozzle=100 K
measurement
vx (m/s)
Tx (K)
1278±8±13
19.0±1.1±0.9
DSMC (original) 1334±12+5-15
DSMC (altered)
1371±2+5-15
v (m/s)
33.3±1.6+0-3
1436
19.0±0.2+0-3
1436
Partially Dissociated Beams
 DSMC calculation of an H/H2 expansion with Q=1 mbarl/s, a=0.63
and Tnozzle=100 K
H1
H2
vx (m/s)
Tx (K)
measurement atoms
1750±47±24
25.7±4.9±1.5
DSMC atoms
1760±20+6-19
41.0±3.4+0-3
measurement molecules
1579±51±17
23.7±7.1±1.0
DSMC molecules
1590±33+6-17
44.0±4.3+0-3
v (m/s)
2031
1436
Partially Dissociated Beams
 Energy and enthalpy considerations for an expanding beam with only
translational degrees of freedom lead to the balance equation (see also
H.Haberland et al. Rev.Sci.Instr. 56, (1985) 1712):
5
1
3
k BT0  mv 2x  k BT  k BT
2
2
2
 For T0=Tnozzle one expects:
E Beam
3
5


2 k BTnozzle 2
 DSMC calculations show
incomplete
thermalization of
the gas inside
the nozzle
Density Measurements
 Measurement of intensity profiles of the atomic fraction of the beam
with beam profile monitor (A.Vassiliev et al., Int. Workshop on
Pol.Sources and Targets, Erlangen 1999, Procs. Page 200)
 2 x 16 gold plated tungsten wires of diameter dw=5mm and 2 mm
spacing
 Calculation of deposited power from the recombination of DSMC
calculated atomic density and velocity distributions
 Power calibration of the wires  the expected resistance change
 Comparision with measurement
Partially Dissociated Beams
Density and velocity distributions from DSMC
measured
Partially Dissociated Beams
Calculated (circles) and measured (triangles) wire resistances
Q = 2 mbarl/s
Q = 1 mbarl/s
10 mm distance
20 mm distance
nozzle  beam profile monitor
The hollow carrier jet
 Proposed by V.L.Varentsov et al., 7th Int. Workshop on Pol. Gas Targets
and Pol. Beams, Urbana, AIP Conf. Procs. 421 (1997) 381
 Supposed to increase intensity of the beam through the collimator
 Cooling and confining of the atomic beam by an overexpanded hollow
carrier jet
 Small mixing and removal of the carrier gas with the skimmer
The hollow carrier jet
Measurements with D2/H2, H/H2 , D/D2 , D/He as inner / carrier gas
D2 w/o H2
D2 with H2
No intensity gain, huge amount of
carrier gas in the detector
H2 density
No cooling effect, but acceleration because of mixing of D2 and H2
The hollow carrier jet
Measurements with Ar/N2 as inner / carrier gas
Ar w/o N2
Ar with N2
High intensity gain, no
carrier gas in the detector
N2 density
Large cooling effect, no acceleration  no mixing
Summary
 DSMC - excellent method to describe the expansion of
gases in the transition region between laminar and
molecular flow
 Results confirmed by several measurements of density
and velocity
 Origin of the discrepancies between measured and
simulated temperature found and solved by modification of
appropriate input parameters of the DSMC
 No observation of the predicted carrier-jet effect for H and
D but for heavier gases
 Explanation of both experimental findings with the DSMC
 Publication accepted by NIM and also available in
arXiv: 0810.0393 [physics.atom-ph]
Outlook
 Use of this method to design a new generation of atomic beam sources
 Optimization of nozzle geometries by implementation of recombination
into the calculations
 Design of improved beam
forming elements
 Implementation of sextupole
magnets into the code to finally
understand the behavior of the
output intensitiy of an ABS
 First step – Use of the DSMC
output parameters for sextupole
tracking Monte Carlo simulations